Minimum Covariance Determinant Estimator and Outlier Detection for Interval-valued Data

TL;DR

This paper introduces a robust estimator for interval-valued data that improves covariance estimation and outlier detection, outperforming classical methods in simulations and real-world applications.

Contribution

It extends the Minimum Covariance Determinant estimator to interval data, providing a robust approach for covariance estimation and outlier detection.

Findings

Robust estimator outperforms classical methods in simulations.

The method effectively detects outliers with adaptive cutoff values.

Application to real datasets demonstrates practical utility.

Abstract

Interval-valued data are one of the most common symbolic data types, which enables the preservation of the underlying variability of the data. The interval mean and covariance matrix can be estimated using the barycenter approach based on the Mallows distance. However, as for conventional data, classical estimates can be significantly affected by anomalous data points, frequently present in real-life datasets. To address this problem, we develop a robust alternative which estimates location and scale by extending the Minimum Covariance Determinant estimator to interval-valued data. The algorithm yields a robust Interval-Mahalanobis distance, which can be used to detect anomalous observations based on adaptive cutoff values. Through extensive simulation studies across various contamination levels, we demonstrate that the interval-valued robust estimator consistently outperforms classical methods in covariance matrix estimation and achieves superior outlier detection accuracy. Finally, the applicability and effectiveness of the proposed method are illustrated through real-world datasets.